Consider a series of punches (junzuki). We are standing in a left shizen danchi with our left hand extended. We are going to step forward and punch with our right. This is like the 8th movement of Fukyugata Ichi.

OK. So in a left shizen dachi, where is our tanden? It is facing about 45 degrees to the right, as are our shoulders. This is a hanmi position. When we complete our right punch, we will be reversed -- our tanden will be facing about 45 degrees to the left, as will be our shoulders.

So, our tanden and shoulders will go from one 45 degree angle to another. Right?

It is not that simple.

As we begin to punch, we will osae (press) with our left hand. This is to occupy the center and prevent the attacker from entering while we punch. As we osae, the alignment of our tanden and shoulders will change -- we will turn to the right until we are almost sideways.

At this time, our shoulders will become aligned -- the right shoulder will be behind the left. In fact, many of our joints will be aligned -- our left hand, wrist, elbow and shoulder, as well as our right shoulder, elbow, wrist, and hand. Our hips will also be aligned, as will be the joints of our legs.

It is almost as if we are holding a spear with our left hand forward. Just as you would thrust a spear in a straight line, so too would you align your joints to execute a straight punch.

Joint alignment is one of the most important aspects of body dynamics.

Getting back to the punch sequence, when we move from a left punch to a right punch, our shoulders do not simply move from one 45 degree angle to another (90 degress in total), they actually first recede to a 90 degree angle, and then move forward to the next 45 degree angle (135 degrees in total).

It is during the extra initial 45 degree angle (from the 90 degree angle back to the original 45 degree angle), that the koshi is used to generate and initiate power. Without the extra initial 45 degree angle, it is very difficult to fire the koshi. And again, the extra initial 45 degree angle (done during the osae), allows us to align our joints -- to get our power in a line.

Of course, actual angles vary and are not exact. My own hanmi is actually a little greater than 45 degrees. Some people might prefer a smaller angle.

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"Karate Jutsu" means "China Hand art". Karate came to Okinawa from China.
Only in the 1930s or so, was the term "Karate" changed to mean "Empty Hand".
"China Hand" was used in Hawaii until after World War II, and is still used in some dojo.